Conjecture Description of Coinflip Completion [efr-U80H]

Let \mathcal {C} be a distributive Cartesian category with countable products. Then the morphisms A \to B of the coinflip completion with countable Kolmogorov products are given by equivalence classes of deterministic maps f: 2^\omega \otimes A \to B (which are morally identified with the map given by composing this with infinite independent coinflips).

The only nontrivial part is to show that these are stable under forming limiting maps into Kolmogorov products.